The bi-quadratic Diophantine equation with five unknown parameters 4 4 2 2 2 E H ( n ( n 1) )( k l ) R is researched for its quasi complex arithmetic values. A few correlations between the solutions and plethora of other figures notably the triangular, pronic, stella octagula and gnomonic notation are effectively portrayed. Keywords: Bi-quadratic, Non-homogeneous, Integer solution, Diophantine equation, Centered square number.